Objective C - angle between 3 CGpoints

Question

I have 3 CGPoints A, B and C. I want to find the angle between AB and BC. I am trying to develop a swipe keyboard and I want to get the points whenever my swipe path changes the angle by a margin

Answer 1

We need vectors representing AB and BC. Then we can compute the angle using the standard formula, which relates the cos of that angle to the dot product divided by the product of the magnitudes...

float angleBetween(CGPoint v, CGPoint a, CGPoint b) {
    CGVector vA = vectorFromTo(v, a);
    CGVector vB = vectorFromTo(v, b);
    return acosf(dot(vA, vB) / (magnitude(vA) * magnitude(vB)));
}

Here's how to make a vector from a pair of points...

CGVector vectorFromTo(CGPoint from, CGPoint to) {
    return CGVectorMake(to.x-from.x, to.y-from.y);
}

Here's how to dot product two vectors...

float dot(CGVector a, CGVector b) {
    return a.dx*b.dx + a.dy*b.dy;
}

And here's how to compute magnitude...

float magnitude(CGVector v) {
    return sqrtf(v.dx*v.dx + v.dy*v.dy);
}